## Function

f(x,y) = px+qy

## Domain

xandyare elements of the set of allReal numbers

## Graphs

## Derivative

With respect tox:p

With respect toy:qCritical points are formed where the two derivatives equal 0. These critical points may be minimums, maximums, or saddle points. In the first graph, for

x,p= 1 and will never equal 0. Therefore, there will be no critical points for this graph. This is shown since there is no saddle point and the curve goes from negative to positive infinity.

## Integral

With respect tox:(^{1}/_{2})px^{2}+ qxy

With respect toy:pxy + (^{1}/_{2})qy^{2}

## Interesting Features

This function is a plane that goes up on an angle right in the middle of the axis. The plane is "flat" and has a constant slope. The value of

pcauses the table to tilt one way while theqvalues tilts it in the opposite direction.

Back to top

Back to main page